Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 15 (2010), paper no. 12, 119-123.
On Fixation of Activated Random Walks
We prove that for the Activated Random Walks model on transitive unimodular graphs, if there is fixation, then every particle eventually fixates, almost surely. We deduce that the critical density is at most 1. Our methods apply for much more general processes on unimodular graphs. Roughly put, our result apply whenever the path of each particle has an automorphism invariant distribution and is independent of other particles' paths, and the interaction between particles is automorphism invariant and local. In particular, we do not require the particles path distribution to be Markovian. This allows us to answer a question of Rolla and Sidoravicius, in a more general setting then had been previously known (by Shellef).
Electron. Commun. Probab., Volume 15 (2010), paper no. 12, 119-123.
Accepted: 26 April 2010
First available in Project Euclid: 6 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
This work is licensed under aCreative Commons Attribution 3.0 License.
Gurel-Gurevich, Ori; Amir, Gideon. On Fixation of Activated Random Walks. Electron. Commun. Probab. 15 (2010), paper no. 12, 119--123. doi:10.1214/ECP.v15-1536. https://projecteuclid.org/euclid.ecp/1465243955